We visited these two cities as part of a longer road trip during Eliana's spring break.  Innsbruck was a 1 night stopover on our way to Salzburg.  Let's start with Salzburg.

Salzburg, Austria
When I think of Salzburg I think of the Sound of Music.  Eliana and I love the movie (and the soundtrack) so we made sure to do the Sound of Music Tour and see as many of the sights as we could.
We even stayed in a hotel that was once the home where the Sound of Music was filmed:
The grounds were impeccably manicured and looked just as they did in the movie scenes.  The children loved running through the hedges that were almost like mazes.  Eliana liked re-enacting some of the scenes such as the salute while standing in front of the lake after all of the children had fallen in, or on the balcony overlooking the courtyard where Captain Von Trapp had looked at Maria from above.
Lucas running around the garden
The hotel we stayed in was Schloss Leopoldskron and was walking distance to downtown Salzburg.  It took us about 20 minutes to walk from the hotel to the outskirts of the downtown area.  I wouldn't change anything about what we did in Salzburg, especially the hotel.  It was spectacular - especially if you are a Sound of Music fan.  We had complimentary breakfast every morning in the ballroom that was very good and you are able to roam about the grounds and inside the many rooms of the home as a guest.  The library in the home is also very nice and has a hidden doorway that leads up to the balcony.  They invite children to look for this doorway after checking in which makes them feel very welcome and special.
At breakfast with her doll, Samantha
From the balcony of the library
We spent quite a bit of time enjoying the hotel and the grounds.  There was a bar where we were able to get drinks and then stroll yard.  The children found a duckling family and a swing hung from a tree very entertaining.  After our large breakfast each morning at the hotel we would walk into town.  We found the convent (abbey) where Maria had first thought she would be a nun.  We visited the castle and strolled through its grounds.  And we wandered through downtown Salzburg itself (following Rick Steve's Tour).  We also did the Sound of Music Tour which took us to many of the sights that were filmed at different locations.
The famous gazebo where the song "I am Sixteen" was filmed with Leisl jumping from bench to bench
The church where Maria Von Trapp was married

Inside the church where Maria Von Trapp was married

The fountain where the Von Trapp children ran around the stone edge during the Do-Re-Me Song

The ivy tunnel the children ran through during the Do-Re-Me Song
Nonnberg Abbey - Where Maria was to become a nun
Eliana climbing in the trees that the Von Trapp children were hanging from

The front of the Von Trapp House from the movie (the front and back from the movie were actually 2 different homes)
The gates that Maria pushes through as she sings "I Have Confidence" before entering the Von Trapp house for the first time
Other Salzburg Sights:
The downtown area of Salzburg has many squares and many beautiful buildings and churches.  We attended The Salzburg Cathedral for Easter Sunday Mass.  The inside has beautiful murals on the ceilings down either aisle.  Each mural is a station of the cross.  I had a lot of time to admire them as Lucas fell asleep during the church service and I walked him up and down the aisle repeatedly to keep him asleep during the 2 hour Mass.

View of Salzburg from the walk around the castle walls

Salzburg Castle behind us
We took a horse and buggy ride and listened to the driver as he gave us a tour and history of the city.

We found Mozart's home as a child and ate dinner in his home which has now been transformed into a restaurant.

The walk back to our hotel in the evening was enjoyable as we had views of the castle almost the entire way:
Salzburg Caslte and grounds lit up in the distance behind us - we are almost back to our hotel

Innsbruck, Austria
I almost forget about this gem of a city as I was so wrapped up in Salzburg.  Looking back at our photos I am remembering this city in more detail.  We didn't have a lot of time to explore as it was just a stopover for us on our roadtrip on our way to Salzburg, but we did get about 8 hours to explore.
Eliana strutting in her new outfit purchased here in Innsbruck.  Our Sassy Austrian Milkmaid!
The beautiful colored buildings are the foreground for big mountains that seem to be painted behind them. 
On the main pedestrian only promenade there were several stores and restaurants to choose from.  We ate outside in the middle of the promenade.

We stayed at the Novotel in Innsbruck.  The views from our room were fantastic.
A few other photos and link to album from Austria: